Begin by browning the butter: Place the butter in a large saucepan over medium heat. Stir continuously as the butter melts and starts to sizzle, then turns foamy. Keep whisking as it transitions to a golden amber hue with a nutty scent. Remove from heat as soon as this transformation occurs, transferring the butter to a medium-sized bowl to cool for about 10 minutes, or until it’s cool to the touch.

Once cooled, combine the browned butter and sugars in a mixing bowl using an electric mixer. Blend on medium speed until the mixture is smooth and creamy, about 1 minute. Add the egg, egg yolk, vanilla extract, and Greek yogurt, mixing again until fully incorporated.

In a separate large bowl, whisk together the flour, salt, and baking soda. Gradually fold the dry mixture into the wet ingredients on low speed until just combined. Gently mix in both the semi-sweet and milk chocolate chips, ensuring they are evenly distributed throughout the dough.

Cover the dough and chill in the refrigerator for at least 2 hours, or up to 24 hours. Do not rush this step; chilling is essential for achieving the perfect texture. For easier baking, roll the dough into balls before chilling. If you prefer, you can refrigerate the dough for 10 minutes first, then roll into balls, place on a tray, and chill for an additional 1-2 hours.

Once the dough has sufficiently chilled, preheat the oven to 350°F (175°C) and prepare a baking sheet by lining it with parchment paper. If the dough is too firm, allow it to soften at room temperature for about 20 minutes before shaping into cookies. Using a medium cookie scoop or two heaping tablespoons of dough, form balls of cookie dough and place them 2 inches apart on the prepared baking sheet.

Bake for 9-11 minutes, or until the edges are a light golden brown. The centers may appear slightly undercooked, but they will firm up as the cookies cool. Allow the cookies to rest on the baking sheet for 5 minutes before sprinkling them with Maldon sea salt. Transfer the cookies to a wire rack to cool completely.

This recipe yields approximately 24-36 cookies, depending on the size of the dough balls.